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Did the year zero never exist ?
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~Icon~ ~by~ ~@Double_A@discuss.tchncs.de~
So in your idea there would be year +0 and year -0 before it, right?
Well, AD and BC(E) are the usual notation in this case, but yes. This is distinct from -0 and +0 in computation, because as OP says these are intervals rather than points.
floating point arithmetic on computers does suffer the existence of a negative zero. But it's generally considered an unfortunate consequence of IEEE754.